Since it was first staged more than four years ago, War Horse has enjoyed the kind of success that’s usually reserved for Disney extravaganzas and jukebox musicals. The show, adapted from a 30-year-old children’s novel by the British author Michael Morpurgo, is about Joey, a spirited, rust-coloured stallion sold to the British cavalry during the First World War, and the valiant quest of his young former owner to retrieve him. After premiering at London’s National Theatre in 2007 and shattering box office records, it quickly moved to the West End and then to Broadway, earning the Tony Award for best play last spring.

On paper, War Horse seems like another formulaic tearjerker—a variation on Black Beauty or Seabiscuit, with some trench warfare thrown in. What sets the show apart is its use of puppets: Joey, like the other horses in the play, is a clunky-looking mechanical contraption made of wooden planks and nylon stretched over a corset-like cane frame. He bears little resemblance to a real animal. The three puppeteers who control him make no effort to conceal their presence. The one in charge of major head movements is not even inside the frame of the horse—he stands next to it in full view of the audience.

But from the moment Joey hobbles onstage as a young foal, stick-legged and unsteady, he’s as alive, and emotionally resonant, as any of his human co-stars.

Joey is the creation of the Handspring Puppet Company of South Africa. In 2004, the company created a life-size giraffe puppet for a production called, coincidentally enough, Tall Horse. The British theatre director Tom Morris saw the show and asked Handspring to fashion a rideable equine version of the giraffe for War Horse. Starting with a plank of wood suspended between two men, Handspring designers Adrian Kohler and Basil Jones went through a long process of experimentation before arriving at a lightweight, three-dimensional frame and a lever-based operating system. Joey’s original puppeteers spent months visiting horse farms, watching videos of horses and studying horse psychology to ape the mannerisms, bulk and power of a full-size stallion.

The results are uncanny. Joey stands patiently through stretches of dialogue, craning his neck and poking around for food. He whinnies softly, snorts, flicks his tail and twitches his ears. When stressed, he rears back and neighs, and when sent into battle, he breaks into a heart-pounding, thundering gallop. It’s this counterintuitive realism that makes Joey such a marvel—the play’s ability to make you believe in him is its most staggering achievement.

War Horse’s reliance on old-fashioned screw-and-joint puppetry is an anomaly in this era of hyper-realistic CGI and theatrical pyrotechnics. We watch Pixar movies and can count the characters’ pores, and play immersive, multi-dimensional video games enriched with motion-capture technology. It’s effortless magic, requiring nothing from us except to sit back and marvel at the display. The puppets in War Horse engage the audience on an entirely different level—Joey’s conspicuous puppetness doesn’t merely create an illusion, it adds a degree of wonder missing from attempts at seamless realism. When Joey is injured trying to clear a barbed-wire fence, we feel for him as we would a real horse.

Joey is a throwback to a more engaging form of theatre. The show also flips a defiant middle finger at the laboured theatrical attempts at mimicking movie magic. Historically, theatre has asked its audiences to do some of the heavy imaginative lifting. In The Tempest, a bare stage is a deserted island because Shakespeare says so. In Sarah Ruhl’s Eurydice, a father builds his daughter a room out of one long strand of string. Our mental participation enriches the experience: we get a hand in bringing that theatrical world to life. Film, by contrast, is a much more passive medium—its location scouts, cinematographers and special effects technicians do most of the work, and anything that might disrupt the illusion is digitally erased.

Big-budget theatre, instead of embracing its own limitations and offering an alternative to the perfect realities conjured by film, TV and video games, has gravitated toward splashier, movie-like productions. The strategy has worked on an economic level—theatres are now routinely filled with people who would never have bought tickets to see the latest Neil Simon drama or Sondheim musical—but the result has been an artistic flatline, with more and more marquees touting musical versions of movies best left undisturbed.

Worse, the special effects that are increasingly worked into theatrical productions often flounder onstage. In her film incarnation, Mary Poppins appears to glide ethereally over the foggy rooftops of London. Onstage, this signature moment becomes a far less enchanting zip-line ride into the balcony of the Princess of Wales. Half the thrill of Spider-Man: Turn off the Dark is waiting to see if the cast makes it to the final curtain unharmed. Theatre simply can’t compete on that level—the space is too restrictive, and the proximity of a live audience makes every crack in the façade painfully obvious. Seeing Poppins hanging from the ceiling doesn’t enhance our belief in her magical nature, it kills it.

Mirvish Productions has made a fortune putting on wham-bam theatrical blockbusters, so it’s somewhat ironic that at the centre of its latest hit is a puppet made from a tangle of wood and screws. Puppets embody the collaborative process of the theatre, coaxing the audience to imprint life onto an otherwise inanimate object. They demand the ultimate suspension of disbelief.